THE NET NORMAL FORCE PER CROSSING POINT: A UNIFIED …“crossing points” and decided to calculate...

THE NET NORMAL FORCE PERCROSSING POINT: A UNIFIED

CONCEPT FOR THE LOWCONSISTENCY REFINING OF PULP

SUSPENSIONS

J.-C. Roux*, J.-F. Bloch, R. Bordin and P. Nortier

Laboratoire de Génie des Procédés Papetiers, UMR CNRS 5518, GrenobleINP-Pagora

461 rue de la Papeterie, 38402 Saint Martin d’Hères – FranceTel : +33 476 826 911 – Fax : +33 476 826 933

*Email : [email protected] (corresponding author)

ABSTRACT

The objectives of this article are:

– First, to theoretically propose a unified concept: the net nor-mal force per crossing point,

– Second, to experimentally undertake refining trials on a pilotdisc refiner in order to compare all concepts for the refiningintensity and to validate the chosen one.

We will begin by re-visiting the old concepts of the refining inten-sity, in the low consistency regime. After a theoretical proof basedupon the physics of the phenomena, applied to beaters andindustrial refiners, a unified concept of the refining intensity isproposed and strengthened: the net normal force per crossingpoint.

Then, experimentations are undertaken on a pilot refiner(single disc) in hydracycle (or batch) conditions. More precisely,the effects of the grinding codes and of the average crossing angle

14th Fundamental Research Symposium, Oxford, September 2009 51

Preferred citation: J.-C. Roux, J.-F. Bloch, R. Bordin and P. Nortier. The net normal force per crossing point: A unifi ed concept for the low consistency refi ning of pulp suspensions. In Advances in Pulp and Paper Research, Oxford 2009, Trans. of the XIVth Fund. Res. Symp. Oxford, 2009, (S.J. I’Anson, ed.), pp 51–83, FRC, Manchester, 2018. DOI: 10.15376/frc.2009.1.51.

of the bars are analyzed in a set of 6 refining trials. For theseexperimentations, different engineering concepts of the refiningintensity are compared (specific edge load Bs, specific surface loadSSL, modified edge load MEL, net tangential force per crossingpoint and net normal force per crossing point). These refiningintensities should allow to analysing the cutting kinetics of fibres.

All the chosen engineering concepts reach this goal more or lesshowever the net normal force per crossing point is the best tool.Indeed, through the range of the data concerned, it revealed aclear monotonous evolution with the cutting kinetics on fibres.The more is the net normal force per crossing point, the more isthe cutting effect on fibres.

1 THEORETICAL APPROACH

1.1 Case of a beater

1.1.1 Parallel bars

In the earlier 1887, Jagenberg [1] studied the case of a beater where the barswere parallel to each other and to the axis of the roll as it can be seen onfigure 1. He realized that the bar contact area could have a role in quantify-ing the refining action on fibres. The bar contact area Ac is the real area(m2) obtained when the bars of the roll overlap the bars located on thebedplate.

Figure 1. Geometry of a beater.

52 Session 1: Fibre Preparation

J.-C. Roux, J.-F. Bloch, R. Bordin and P. Nortier

In order to calculate this engineering parameter Ac, we must begin asJagenberg did by defining the variables appearing in figure 1. DR is the diam-eter of the roll (m) and aR, aS are, respectively the width (m) of bars on theroll, named rotor, and the width of bars on the bedplate, named stator. l0 isthe width (m) of the bedplate; in this typical case of parallel bars beater, thewidth of the bedplate is the same as the common length of the bars (m) onthe bedplate or stator bars. nR and nS are, respectively the number of bars onthe roll, and on the bedplate.

Jagenberg performed the fraction of the developed area of the roll coveredby the roll bars at diameter DR, and then this term was multiplied by the areacovered by the stator bars on the bedplate. This calculation gives the barcontact area Ac:

Another expression can be obtained after simplification of the term l0 in thefraction referring to roll parameters.

Jagenberg defined another engineering parameter as the cumulative edgelength Lc since this term appears clearly in equation (2):

Hence, he pointed out two engineering parameters:

– the cumulative edge length Lc (m);– the bar contact area Ac during the overlapping of the roll in front of the

bedplate.

However, he did not write the relation between these two engineering vari-ables Lc and Ac for calculating the cumulative edge length Lc when the barcontact area Ac is known.

By introducing equation (3) in the bar contact area given by equation (2),the relation can be expressed as follows:


The Net Normal Force Per Crossing Point

At this point of our development, it is interesting to find the expressions of nR

the number of bars on the roll and nS the number of bars on the bedplateversus the beater variables as the bar width, aR, aS (m), the bar length l0 (m)and the length of the bedplate Ls (m).

If we complete our description of the beater technology, other variablesmust be introduced as the width of grooves (m), both on the rotor bR and onthe stator bS, see figure 1.

If we replace these expressions of the bar numbers (5) in the equation (2) ofthe bar contact area Ac, we obtain:

This new development leads to define the bar contact area Ac from the globaloverlapping area given by the term between brackets. Hence, a new fractionappears and we will see in further developments that this fraction is alsoobtained in case of the other refining technologies as disc or conical refiners.This fraction only includes the bar width of the rotor aR and that of the statoraS and the groove width of the rotor bR and that of the stator bS.

1.1.2 Inclined bars

In 1906 and 1907, Kirchner [2] and Pfarr [3] gave an accurate calculation ofthe bar contact area in case of inclined bars, both on the roll (rotor) with anangle αR and on the bedplate (stator) with an angle αS.

Kirchner [2] hence demonstrated that the bar contact area Ac was independ-ent of the two angular parameters of bars αR and αS, he obtained the equation(7) identical to equation (6) given for the case of parallel bars.

Pfarr [3] looked after an expression of the bar contact area similar to thatpreviously given by Jagenberg in equation (2). He first calculated the bar



numbers in the case of inclined bars both for the rotor and for the stator andobtained:

Then, by introducing these bar numbers in the Kirchner’s equation (7), Pfarr[3] obtained the expression of the bar contact area for the case of inclined barbeaters:

We can observe the similarity between equations (2) and (9). The last one isonly an extension of the previous written by Jagenberg for the case of parallelbars beater. This can be seen by replacing the angular parameters by 0°.

Is it possible to obtain, similarly, an extension of the cumulative edgelength Lc in case of inclined bars? To answer to this question, we will useequation (4). Then, by replacing Ac given by equation (9) in the linear relation(4), it comes without any ambiguity:

Figure 2. Geometry of the bedplate on a Valley beater.



After simplification, we can obtain the expression of the cumulative edgelength in case of beaters with inclined bars.

If we replace the angular parameters by 0°, the previous expression alreadygiven by Jagenberg is obtained.

The cumulative edge length given by equation (11) yields three moreobservations.

Firstly, this cumulative edge length is found to be independent of geo-metrical angular parameters since the bar contact area is independent ofthese parameters according to Kirchner.

Secondly, the cumulative edge length is an engineering parameter previ-ously defined [4], as the reference edge length LREF (m). Hence, it is the samequantity as the cumulative edge length.

Thirdly, if l0, the width of the bedplate is also the bar length in case ofparallel bars, it is not the bar length in case of inclined bars. The real lengthof inclined bars (different for the rotor and for the stator) seems to appear ina complex manner as follows:

This is probably one reason why there were some misunderstandings in thepast when different authors tried to extend the cumulative edge length frombeaters to disc or conical refiners. We will use at least equation (11) to per-form the calculation of the cumulative edge length for beaters, disc and con-ical refiners.

When αR and αS are different from zero angles (case of inclined bars),during the relative motion of the roll in front of the bedplate, a certainnumber of crossing zones are generated. Kirchner [2] named these zones“crossing points” and decided to calculate their number NCP. He gave theexpression of the area of a single bar crossing point (m2) when the bar angle isknown:

Then, the calculation of the number of crossing points NCP was obtained bythe ratio of the bars contact area Ac by equation (9) by the area of a single bar



crossing point ACP by equation (13). The expression of NCP is also given inBaker’s book [5] in chapter 2.

Again, we developed another relationship between the number of crossingpoints NCP and the cumulative edge length Lc, with the same assumptionsconcerning the angles. It is possible to obtain:

1.1.3 Inclined bars: net normal force per crossing point

Roux and his co-workers [4] introduced the concept of net normal force (N)and refining intensity (N) for a beater. They calculated the net normal forceby the following formula which includes the global friction coefficient f:

In equation (16), Pnet is the net power consumed by the refiner and N is therotation speed of the rotor. Now, dividing the net normal force by the numberof crossing points NCP, as given by equations (14) or (15), it was possible toquantify the net normal force per crossing point.

From equation (14), we obtain the following expression of the net normalforce per crossing point given by equation (17):

The expression between brackets in the denominator was empirically intro-duced by Meltzer [6], as the “extended edge length”. He considered “theprojected bar length as the efficiency of a bar to cross counterbars”. Ourtheoretical approach naturally introduces the concept of extended edgelength already proposed by Meltzer and then adds to its legitimacy.

The net normal force per crossing point is our candidate for describing therefining intensity in the low consistency refining process of pulp suspensions.

If the equation (15) is chosen to quantify the number of crossing points



NCP, then a new expression of the net normal force per crossing point can befound, given by equation (18).

It is noted that the numerator is simply the Specific Edge Load, Bs, (J/m or N)defined lately by Brecht and Siewert [8].

However, as the cumulative edge length and the reference edge length arethe same physical quantity, the specific edge load is also the same quantity asthe reference specific edge load, already introduced in [4]. Again, this addslegitimacy to the concept of the reference specific edge load that is exactly thesame as the specific edge load.

However, we must admit that the specific edge load is not sufficient toadequately describe the refining intensity since two adding parameters areinfluencing variables in equation (18):

– the global friction coefficient f of the pulp versus bar materials;– the sinus of the bar crossing angle given by the algebraic sum αR + αS.

1.2 Disc refiner analysis

1.2.1 The cumulative edge length

The extrapolation of the cumulative edge length was proposed in 1958 byWultsch and Flucher [7]. They introduced the following well known expres-sion [5], to calculate the cumulative edge length per revolution (m):

A new variable l̄ was introduced: the average bar length (m). Their under-standing was based upon a proposed extension of Jagenberg’s equation (3) asstated in Baker’s book [5].

Later, Brecht and Siewert [8] used the expression (19) to calculate theSpecific Edge Load Bs (J/m) by equation (20), following the initial ideas ofWultsch and Flucher:

However, our understanding of the cumulative edge length for disc refiners issomewhat different. At first glance, we already demonstrated in this article



that the extension of the cumulative edge length for the beaters in case ofinclined bars was given by equation (11). This last one differs from equation(19) where the average bar length l̄ is not clearly defined.

We propose to clarify the concept of the cumulative edge length, in the caseof a disc refiner, through a physical analogy between a slice of the beater andan elementary annulus of disc.

On figure 3, the pulp suspension motion in the beater occurs in the planeformed by two unit vectors (→iρ , →iψ ), perpendicular to the roll axis. Now, ifwe consider a slice of the beater in the direction of the unit vector →iz , itmeans that the width of the bedplate is also the width of the slice beater dl0.The determination of the elementary cumulative edge length dLc for thisslice of the beater is given by equation (11) written in a differential form asfollows:

For a beater, the bar numbers are independent of the slice of the beater asmentioned previously. So, the integration of equation (21) is easy to performwith this type of technology and leads to equation (11) already mentionedthrough a global understanding at the beginning of this article.

Figure 3. Slice of a beater.



On figure 4, we drew an elementary annulus comprised between the radius ρand the radius ρ + dρ. The pulp suspension motion is supposed to be circularwith this type of disc refiner in the direction of the unit vector →iψ , for eachradius, analogous to the case of a beater.

However, the major difficulty with a disc refiner is given by the differentsituations that occur with time during the relative motion of the rotor disc infront of the stator disc.

In that case, how the bar angles for both the rotor and the stator, may bedefined? If one expression must be used for extrapolation, it should be thatgiven by equation (21), which is certainly not yet currently used in the indus-trial practice.

A careful consideration of the disc geometry, as it was done for example in[9], can lead to the local determination of the numbers of bars on the rotor nR

and on the stator nS as function of the local radius ρ with the corresponding

Figure 4. Elementary annulus of a disc plate for a disc refinerρi ≤ ρ ≤ ρe.



angles ΦR and ΦS for the bar inclinations for the rotor and the stator,respectively:

An analogous form of equation (21), between a slice of the beater and anannulus of a disc refiner leads to the calculation of the elementary cumulativeedge length, by substituting dl0 by dρ.

Hence, in order to find the expression of the cumulative edge length for a discrefiner, integration must be performed over the refining annulus, limited bythe internal radius ρi (m) and the external radius ρe (m), using equations (22)and (23).

Some observations can be given. Equation (24) reveals that Lc is independentof the bar angles on the rotor and on the stator. It confirms the result alreadyobtained by Kirchner when beaters with inclined bars were considered, seeequation (11).

The cumulative edge length is the same physical quantity as the referenceedge length already introduced in [9], since it appeared naturally in the calcu-lations. However, in this article, it is demonstrated through a physical analogybetween beaters and disc refiners. The correct extrapolation of equation (11)for beaters to industrial disc refiners and their complex geometry is given byequation (24).

If we follow the equation (19) for the practical calculation of the cuttingedge length, we should evaluate this quantity by the following:

In this expression, the disc corona is divided in p elementary annulus where



the determination of the bar numbers on the rotor nRk, on the stator nSk isperformed for each annulus. All these numbers are then combined in order togive the cutting edge length (CEL) according to equation (25).

Due to differences in case of inclined bars between the practical determin-ation of the CEL given by the formula (25) and real measurements, the StockPreparation TAPPI Committee decided to include some cosines terms in theexpression (25). The next expression (26) is given for example, in the Tech-nical Information Papers of the TAPPI Association for the determination ofthe cutting edge length (CEL):

In this last equation, average angles for the rotor and the stator are empiric-ally introduced, which could give an expression “close to” our theoreticalsolution.

However, we suggest using the proposed equation (24) which has sometheoretical justification instead of the empirical expression, given by equation(26). Furthermore, in the TAPPI expression, both set variables are gatheredangular and non angular parameters.

In the proposed equation (24), no reference is made to angular parameters,so we need to complete our physical analysis to “naturally” introduce theseangular parameters, this will be done in the next paragraph.

1.2.2 The net normal force per crossing point

Equation (16) gives the net normal force versus the net power consumed for abeater; this expression includes a tangential velocity in the denominator. Ifone wants to develop a similar tangential velocity equation for a disc refiner;we must find its equivalent diameter or radius.

This can be done by calculating, over the disc annulus, the average tangen-tial velocity defined as follows [10]:

Hence, the average radius <ρ> (m) is given by the expression:



Dividing the net normal force by the number of crossing points requires thedetermination of this last number. Due to complex geometrical situationsoccurring in the rotating motion of the rotor in front of the stator, it is onlyan average calculation of this number which is performed.

The average number of crossing points NCP was already calculated by Roux[9] and its expression reduced to a simplified one in the case of a small sectorangle:

Now, the last step is the determination of the net normal force per crossingpoint, calculated on the average, for a disc refiner, by introducing the averageradius – equation (28) and the average number of crossing points – equation(29), we finally obtain:

Again, some observations can be drawn. The numerator of the net normalforce per crossing point is the reference specific edge load or the specific edgeload since these variables express the same physical quantity: the net energyper unit length of bar edge (J/m) or (N).

This quantity: the numerator does not contain any angular parameter.These last variables are included in the denominator. In the previous TAPPIexpression (26), all the variables were gathered but, in fact, there aredecoupled in equation (30).

The physical analogy obtained between equations (18) and (30) is the cleardemonstration that the refining intensity chosen as the net normal force percrossing point is a unified concept.

It can be applied to different technologies as a beater or an industrial discrefiner with different geometries.

The case of a conical refiner, not treated here, may be treated exactly in thesame way.



2 INTERPRETATIONS OF THE INDUSTRIAL PARAMETERS

2.1 Description of the refining installation

The refining trials were undertaken on our Laboratory pilot installation [10,11], as described on figure 5. The pilot is equipped with a single disc refiner(SD) running in hydracycle mode.

It means that the refining energy is distributed to the pulp suspension incycles. The refiner is an automated process with gap clearance sensor andaxial force sensor. This specific metrology was previously described in [12]and will not be detailed in this article. It allows us to measuring the nor-mal and tangential forces and to deducing both the global frictioncoefficient.

In order to define the different engineering parameters which will be modi-fied during the set of refining trials, we must first remind the geometricalconfiguration of a disc plate, as shown on figure 6.

In this typical design, a given sector is composed of parallel bars in anannulus comprised of an internal radius ρi and an external radius ρe. Onthis drawing, the sector has an angular periodicity of 6 per revolutionmeaning that the sector angle is equal to θ = 60°. Usually, the sector angle iscommon for the rotor and the stator. On figure 6, the angle of the first bar,located at the right side, is named the “grinding angle” and written byconvention: α for the rotor disc and β for the stator disc. The understandingof the angular parameters is the same for the rotor or the stator in a firstglance.

Depending on the bar chosen for the rotor disc, the bar inclination angle isvarying from α to α + θ. Hence, a typical value of the bar inclination angle,

Figure 5. Laboratory refining installation.



for each sector (rotor or stator) is given by the average value, we then obtainthe following expressions:

If a rotor plate is superimposed in front of a stator plate, by considering theaverage value for each plate, the angle of the bar crossings is defined asfollows:

On the one hand, the quantification of the average angle for the entire barcrossings is obtained by replacing the terms of equations (31) in equation(32):

On the other hand, the number of bars located at a given radius ρk can beanalytically calculated, by introducing the previous angles ΦR and ΦS in thefollowing expressions given for the rotor, then for the stator:

Figure 6. Geometrical patterns of a sector on a disc plate.



2.2 Description of the refining conditions

The pulp suspension tested in these investigations was a market pulp of nonbleached Kraft Canadian softwood. Neither the characterization of the pulpnor the essence was undertaken since our aim in this article was based uponan assessment of engineering parameters.

During the six refining trials, the dry mass of the pulp in the tank was thesame at m = 14 kg and the solid consistency chosen at C = 3.5% (or 35 kg/m3).A constant volumetric flow measured by the flow meter was kept at Q = 10m3/h. Hence, the time period of a cycle was constant at V/Q = 2.4 min (or144 s).

The refining trials were undertaken on the same single disc refiner with thefollowing engineering parameters: internal radius ρi = 0.065 m; externalradius ρe = 0.150 m. These values allow the calculations of the ratio k of theinternal to the external radius of the annulus:

and that of the average radius < ρ >, considering the equation (28) rewrittenby using the previous ratio:

The net power was kept constant during one refining trial. The rotation speedof the refiner was also taken at a constant value for all the refining trials:N = 1500 rev/min or 25 rev/s.

For the disc plates, made of stainless steel, the groove depth was constantat 6.4 mm, corresponding to a grinding code of either (2-2-4) or (3-3-4)expressed classically in sixteenth of inches. We remind to our reader that thegrinding code is classically a set of 3 numerical values (a-b-c), respectively:



the bar width, the groove width and the groove depth (or the bar height). (2-2-4) is often used for short fibres and (3-3-4) privileges long fibres.

The sector angle was also the same during all the refining trials, a commonvalue for both rotor and stator disc was chosen at θ = 22.5°, leading to anangular periodicity of 16 sectors per revolution for one disc plate.

2.3 Description of variable engineering parameters

The engineering parameters chosen for these investigations were:

– the common value of the bar width and groove width: a = b;– the net power constant during one given trial Pnet;– the sum of the grinding angle of the rotor and the stator: α + β.

In table 1, we have gathered these different numerical values, completed bythe average crossing angle γ, given by equation (32):

The sum of the grinding angles α + β was chosen for two different numericalvalues:

– a so-called “cutting” geometry where α = + 5° and β = − 5°;– a so-called “fibrillating” geometry where α = + 10° and β = + 15°.

As it was previously mentioned in [9], the refining intensities defined bydifferent authors in the paper literature are always proportional to the netpower applied. The bar width a and the average angle γ of the bar crossingsare also known to be influent variables for characterizing the refining effectson fibres.

Table 1. Description of the chosen engineering parameters in the refining trials

Trial n° a = b[mm]

Pnet

[kW]α + β[°]

γ = α + β + θ[°]

R

[δ]S

[°]

1 3.2 16.6 0 22.5 16.25 6.252 3.2 9.6 0 22.5 16.25 6.253 4.8 12 25 47.5 21.25 26.254 4.8 7 25 47.5 21.25 26.255 4.8 12.4 0 22.5 16.25 6.256 4.8 24 0 22.5 16.25 6.25



2.4 Determination of different refining intensities

For all the refining trials specified by table 1, we propose to calculate thedifferent refining intensities in the following order: the specific edge load [8],the specific edge load recommended according to the TAPPI engineeringrules, the specific surface load [13], the modified edge load [6], the net tangen-tial force per crossing point [9], the net normal force per crossing point [9].

2.4.1 Determination of the specific edge load

If we combine equations (20) and (24) with the correct quantification of thecumulative edge length, the determination of the specific edge load Bs is thengiven by the following expressions:

Two different bar widths (or groove widths) and six different net powers leadto consider a refining intensity in a range of 1 to 5.6.

2.4.2 Determination of the specific edge load according to TAPPI rules

As it is proved in this article, no angular parameter can be found in equation(37). TAPPI rules proposed to empirically introduce the angular parametersas described in the following developments:

According to these rules, the calculation of the specific edge load can be doneafter the primary determination of the edge length both for the rotor ELR andthe stator ELS.

The edge length for the rotor and the stator are the respective expressionsunder square root signs in equations (38). For sake of simplification, weconsider that the bar width a, respectively the groove width b, are the same forthe rotor and the stator. In equations (38), the disc corona is divided in p



elementary annulus. The edge length for the rotor ELR can be determinedwith the help of equation (34) that counts the bar number on a given annulus:

The calculation of the edge length for the stator ELS is formally the same asthat for the rotor. If a continuous expression is preferred rather than a dis-crete one, the cutting edge length CEL is then given by the following equationafter integration over the global corona:

This last expression allows the final determination of the specific edge loadaccording to TAPPI rules:

This expression empirically introduces the angular parameters that combinegrinding angles and the sector angle as previously given by equations (31).

2.4.3 Determination of the specific surface load

Lumiainen [13] claimed that the bar width and the average crossing anglemust be taken into account for a more precise quantification of the refiningintensity. He also gave the general formula to calculate the specific surfaceload:

In case of the same bar width for the rotor and the stator, the formula issimplified to the following expression:



All the engineering parameters are empirically included in this definition ofthe refining intensity.

2.4.4 Determination of the modified edge load

With this refining intensity given by Meltzer [6], the modified edge loadincludes the bar width, the groove width and the average crossing angle as it isexpressed in the general case:

When the bar width and the groove width are the same, this equation can besimplified and the bar width then disappears, it only remains in the expressionof the specific edge load Bs:

2.4.5 Determination of the net tangential force per crossing point

This quantity can be obtained in two steps. Firstly, the net tangential force isdeduced from the net power applied and the average tangential velocity asexpressed by equation (27):

Secondly, the average number of crossing points is calculated precisely withthe following equations already given by Roux in [9]:

After replacement of the average number of crossing points in the expressionof the net tangential force per crossing point, we obtain the following equa-tion which can be practically used to calculate the required value:



2.4.6 Determination of the net normal force per crossing point

The authors of this article have theoretically demonstrated that the unifiedconcept for quantifying the refining intensity was the net normal force percrossing point. In fact, it means that a physical term is lacking, this term is theglobal friction coefficient f. The expression of the net normal force per cross-ing point hence comes:

2.4.7 Observations on the different refining intensities

Some general observations can be drawn after calculation of the differentcandidates for the refining intensity. All the refining intensities, except thespecific edge load, incorporate angular parameters. The specific surface loadincludes one more engineering parameter: the bar width on the average. Themodified edge load includes the bar width and the groove width.

However, the net normal force per crossing point incorporates a new phys-ical quantity that has never been introduced before (except by the authorsthemselves): the global friction coefficient.

Our last step is then to calculate the candidates for quantifying the refiningintensity on fibres during the pulp refining in low consistency regime.

2.5 Calculation of different refining intensities

We have gathered all the empirical and physical quantities in table 2 in orderto see if they are classified in the same order for the 6 refining trials under-taken on our pilot.

Some observations can be given. First, the star angle γ* is very close to theaverage crossing angle γ as it can be seen through a comparison between thenumerical values for all the six refining trials in tables 1 and 2. Second, thecutting speed Lc.N shares the refining trials in two categories: (1,2) and(3,4,5,6) whereas the average number of crossing points NCP leads to threecategories: (1,2), (3,4), (5,6). At this point, we can observe that the level ofdiscrimination is better by using concepts that incorporate angularparameters.



Tab

le 2

.C

alcu

lati

on o

f th

e di

ffer

ent

refin

ing

inte

nsit

ies

Tri

aln°

a[m

m]

Pne

t

[kW

]γ* [°

]f

Lc.N

[km

/s]

NC

PB

s

[J/m

]B

sTap

pi

[J/m

]S

SL

[J/m

2 ]M

EL

[J/m

]F

net

t/N

CP

[N]

Fne

tn

/NC

P

[N]

13.

216

.622

.20.

1525

.296

537.

910.

656

0.67

220

2.7

3.29

91.

737

11.5

82

3.2

9.6

22.2

0.18

25.2

9653

7.91

0.38

00.

388

117.

21.

908

1.00

55.

583

4.8

1246

.70.

2011

.243

460.

601.

067

1.16

720

5.1

2.42

61.

466

7.33

44.

87

46.7

0.25

11.2

4346

0.60

0.62

30.

681

119.

71.

415

0.85

53.

425

4.8

12.4

22.2

0.13

11.2

4323

9.07

1.10

31.

129

227.

15.

545

2.91

922

.45

64.

824

22.2

0.16

11.2

4323

9.07

2.13

52.

185

439.

610

.73

5.65

135

.32



Third, for all the refining trials undertaken, the different chosen refiningintensities cover a range of 1 to 6, which is sufficiently representative for abench-mark.

Fourth, the best discriminating refining intensities among the six candi-dates are given by the three last columns. This result is proved when onewants to classify the trial numbers from the smallest to the highest refiningintensity; we obtain for the six different candidates:

If we remind that the specific edge load, its calculation according to TAPPIengineering rules and the specific surface load are empirical concepts, we arenot surprised by the results obtained. None of this candidate leads to thesame classification as the others.

So, it is clear that these tools should be used with great care for a quantifi-cation of the refining effects on fibres, specially the shortening effect on fibres.

3 PRACTICAL RESULTS

3.1 Cutting kinetics of fibres

Among the main refining effects, the cutting on the fibres is more directlyrelated to the refining intensity. Hence, the refining intensity concept was firstdeveloped in order to quantify this shortening effect on fibres. Our purpose isto find the refining intensity which would be the best tool to quantify thecutting kinetics on fibres, among the six possible refining intensities presentedin this article.

3.2 Experimental results

For one given refining trial, the average weighted fibre length Lf was measuredwith a Morfi analyser at different times, which means at different specific

Table 3. Classification of the refining trials by increasing the refining intensity

Refining Intensity Classification of the trial numbers towards increasingintensity

Bs 2 < 4 < 1 < 3 < 5 < 6Bs-Tappi 2 < 1 < 4 < 5 < 3 < 6SSL 2 < 4 < 1 < 3 < 5 < 6

MEL 4 < 2 < 3 < 1 < 5 < 6Fnet

t /NCP 4 < 2 < 3 < 1 < 5 < 6Fnet

n /NCP 4 < 2 < 3 < 1 < 5 < 6



energies consumed by the pulp. The six refining trials are performed with aconstant net power applied Pnet and a constant rotation speed N as it waspreviously presented in paragraph 2.2. The following tables summarise thedata obtained for the six refining trials.

Table 4. Pulp properties versus net specific energy for refining trial n°1

Pulp propertyE net

sp [kWh/T]

0 63.4 146.8 192.2

Lf [mm] 2.158 2.034 1.840 1.739°SR 15 18 27 38

WRV [g/100g] 108 129 150 162


Pulp propertyE net

sp [kWh/T]

0 88.6 168.5 258.8

Lf [mm] 2.158 2.094 1.959 1.820°SR 15 19.5 28.5 43

WRV [g/100g] 108 133 152 167


Pulp propertyE net

sp [kWh/T]

0 87.9 176.7 266.5

Lf [mm] 2.158 2.103 1.900 1.692°SR 15 19.5 31.5 52.5

WRV [g/100g] 108 143 165 186



In this article, we will only investigate on the cutting effect on fibres and willanalyse the other main effects (fibrillation and hydration) in futurepublications.

All results can be condensed in the same figure for an assessment of thecutting kinetics on fibres for all the experimental trials performed.


Pulp propertyE net

sp [kWh/T]

0 104.4 201.7 276

Lf [mm] 2.158 2.118 2.003 1.868°SR 15 20 31.5 43

WRV [g/100g] 108 144 165 176


Pulp propertyE net

sp [kWh/T]

0 89.2 180 267.8

Lf [mm] 2.158 1.855 1.478 1.021°SR 15 20 40 70

WRV [g/100g] 108 135 163 192


Pulp propertyE net

sp [kWh/T]

0 88.5 180 258

Lf [mm] 2.158 1.623 1.138 0.896°SR 15 21 45 63

WRV [g/100g] 108 137 163 181



3.3 Empirical modelling of the cutting kinetics

For the range of specific energy concerned by these refining trials, a secondorder model fits adequately the experimental average weighted fibre length.Hence, the following equation applies with a good precision for all the refin-ing trials performed. For the refining trial n°k:

This empirical model is then used to interpolate the average weighted fibrelength Lf−k (for the refining trial n° k) at the same net specific energy con-sumption chosen: 150 kWh/T.

All the calculated data are summarised in table 10.

The refining trial number 6 was performed with the highest refining intensityas it is proved by table 3, whatever the candidate used for defining this refiningintensity. The positive sign of the coefficient a6 means a change in the curva-ture of the cutting kinetics on fibres, compared to the other coefficients, froma1 to a5, as it can be observed on figure 7.

With table 10, the six refining trials can be classified from the smallest tothe highest cutting effect on fibre: 4 < 2 < 3 < 1 < 5 < 6.

Hence, in a first approach, this range obtained can be compared with thedifferent classifications already given by table 3. The three last candidates fordefining the refining intensity: the modified edge load MEL, the net tangen-tial force per crossing point F net

t /NCP, the net normal force per crossing pointF net

n /NCP succeed to evaluate the cutting effect on fibres.

Table 10. Interpolation of the average weighted fibre length Lf−k for E netsp = 150 kWh/T

and for the six refining trials

Trial n°k; k 1 2 3 4 5 6

10+6.ak −0.458 −2.546 −4.971 −3.863 −4.992 +7.97910+4.bk −20.42 −6.646 −4.521 +0.142 −29.03 −69.82

r2k 0.9987 0.9932 0.9917 1.0000 1.0000 0.9999

Lf−k(150kWh/T)[mm]

1.841 2.001 1.978 2.073 1.610 1.290



3.4 Benchmark of the different refining intensities

In order to determine the level of understanding which is obtained with onegiven refining intensity, we will compare the different average weighted fibrelength (at 150 kWh/T) for the six refining intensities.

A graphic interpretation will be privileged since it is the simplest one forperforming the benchmark. In order to prepare the analysis, all the data aregathered in table 11.

We will show in the following developments the “clouds” of points betweenthe different values of fibre length and that of refining intensity.

If we find a linear relationship between the fibre length and the correspond-ing refining intensity, it will mean that the refining intensity can be a goodtool to quantifying the cutting effect on fibres.

Figure 7. Experimental results for the six refining trials.

Table 11. Data required for benchmarking the refining intensities

Trialn°

Lf−k(150kWh/T)[mm]

Bs [J/m] Bs-Tappi

[J/m]SSL

[J/m2]MEL[J/m]

F nett /NCP

[N]F net

n /NCP

[N]

1 1.841 0.656 0.672 202.7 3.299 1.737 11.582 2.001 0.380 0.388 117.2 1.908 1.005 5.583 1.978 1.067 1.167 205.1 2.426 1.466 7.334 2.073 0.623 0.681 119.7 1.415 0.855 3.425 1.610 1.103 1.129 227.1 5.545 2.919 22.456 1.290 2.135 2.185 439.6 10.73 5.651 35.32



Case of the specific edge load Bs

Case of the specific edge load according to TAPPI engineering rules

At this point, neither the specific edge load nor its corrected value accordingto the TAPPI engineering rules is able to account for the understanding ofthe cutting kinetics on fibres. This result could have been observed in table 3where the classification of the refining intensity was not in the same order asthe cutting kinetics on fibres.

Figure 8. Correlation between the average weighted fibre length at E netsp = 150 kWh/T

and the Specific Edge Load Bs.

Figure 9. Correlation between the average weighted fibre length at E netsp = 150 kWh/T

and the Specific Edge Load Bs-TAPPI.



Hence, it could be adventurous to use in the paper industry these conceptsalone to quantify the cutting effect on fibres.

Case of the specific surface load SSL

If the regression coefficient is better with the specific surface load than thatwith the two previous cases, it is also clear that the discriminating nature ofthis intensity is lost. At least, two pairs of fibre length cannot be discrimin-ated with this tool as seen in figure 10.

Case of the modified edge load MEL

Figure 10. Correlation between the average weighted fibre length at E netsp = 150 kWh/

T and the Specific Edge Load SSL.


T and the Modified Edge Load MEL.



Case of the net tangential force per crossing point F nett /NCP

Case of the net normal force per crossing point F netn /NCP

As it was predicted from table 3 and from the experimental classification ofthe fibre length, the modified edge load, the net tangential force per crossingpoint and the net normal force per crossing point can be 3 success tools toquantify the cutting effect on fibres.


T and the net tangential force per crossing point F nett /NCP.


T and the net tangential force per crossing point F netn /NCP.



In this article, we have developed a unified physical refining theory whichputs the emphasis on the net normal force per crossing point. Our reader isprobably now convinced that this is the best refining intensity for the inter-pretation of the cutting kinetics on fibres. Even if the results with the nettangential force are acceptable, the introduction of the global friction coef-ficient is of primary importance in understanding the cutting effect on fibres.

We also have proved that the normal forces are responsible for the cuttingon fibres and that the terminology often used in the industry of “cuttingangle” should be eliminated definitely, we prefer to use crossing angle, whichis exactly what it is, nothing more.

This classification of the cutting effect on fibres with these data is mon-otonous with the proposed refining intensity that is to say the net normalforce per crossing point. The more the net normal force per crossing point,the more pronounced will be the cutting effect on fibres.

The average crossing angle is not the only influencing variable since thespecific edge load on one hand and the global friction coefficient on the otherhand counterbalance its effect, see equation (49) that is reminded in a simpli-fied form:

When one wants to verify if a model takes correctly into account the experi-mental data, the parity diagram is an interesting tool for this purpose.

A parity diagram is given on figure 14 between the estimated fibre length

Figure 14. Parity diagram for the estimation of the average fibre length at 150 kWh/Tby using the net normal force per crossing point as refining intensity



and the measured fibre length (or the values interpolated when unknowndirectly). Hence, the knowledge of the refining intensity: the net normal forceper crossing point is sufficient to quantify and predict the cutting effect onfibres.

CONCLUSIONS

In this article, we have proposed to revisit the earlier knowledge of the refin-ing operation of pulp fibre suspension in low consistency range when it wasoperated on beater equipments.

By considering the relation between the cutting edge length and the barcontact area, two fundamental variables introduced previously by Jagenberg,it was possible to theoretically justify the extrapolations:

– in a first step, from a beater with parallel bars to a beater with inclined bars;– in a second step, from a beater with inclined bars to a disc with inclined

bars also.

This last extrapolation based initially on geometrical concepts was furtherjustified by the physical analogy that exists between a slice of the beater andan elementary annulus of disc plates.

In the literature, it is possible to find different concepts for assessing the“refining intensity”. A benchmark was undertaken considering the mostfamous practical refining intensities as the Specific Edge Load (Bs), its specificvalue according to the TAPPI engineering rules (Bs-TAPPI), the SpecificSurface Load (SSL), the Modified Edge Load (MEL), the net tangentialforce per crossing point (F net

t /NCP) and the net normal force per crossing point(F net

n /NCP).Six refining trials were carried out on our refining pilot under hydracycle

conditions.Two bar widths and two average bar crossing angles were investigated.

These refining trials were compared considering the shortening effect onfibres at the same net specific energy consumption of 150 kWh/T.

The results lead to the conclusion that three tools can be used as refiningintensity to quantify the cutting effect on fibres: the modified edge load, thenet tangential force per crossing point and the net normal force per crossingpoint. However, the net normal force per crossing point that results from ourrefining physical theory has the best monotonous variation with the shorten-ing kinetics on fibres. It is graphically proved in this publication. All the otherrefining intensities were not sufficient in quantifying this shortening effect onfibres.



Another conclusion can be drawn from these results: the reference cumula-tive edge length and the cumulative edge length are definitely the same quan-tity. It is also the case for the reference specific edge load and the specific edgeload which are identical. However, none of them include angular parameters

The specific edge load in fact is not sufficient to interpret the refining effectson fibres. Indeed, the global friction coefficient and at least the average cross-ing angle must be taken into account.

All these variables are considered in the net normal force per crossingpoint, a unified physical concept for correctly describing the intensity of thecutting on fibres, on equipments as different as beaters, disc or conicalrefiners.

BIBLIOGRAPHY

1. F. Jagenberg. Das Höllandergeschirr in Briefen an einen Papiermacher, 1887.2. E. Kirchner. Das Papier. 4 Teil Ganzstoffe, 1906.3. A. Pfarr. Holländer und deren Kraftverbrauch. Wochenblatt für Papierfabrika-

tion 35:3032–3039, 1907.4. J.-C. Roux, J.-F. Bloch and P. Nortier. A kinetic model for pulp refining, includ-

ing the angular parameters of the equipment. Appita Journal 60(1):29–34, 2007.5. C. Baker. Refining Technology, (ed. C. Baker), published by PIRA International

Ltd, Leatherhead, 2000.6. F. Meltzer. Key figures for the assessment of the refining process. Ch. 2 in Refin-

ing Technology (ed. C. Baker), PIRA International Ltd Publishing, Leatherhead,2000.

7. F. Wultsch and W. Flucher. Der Escher-Wyss-Kleinrefiner als Standard-Prüfgerät für moderne Stoffaufbereitungsanlagen. Das Papier 13(12):334–342,1958.

8. W. Brecht and W.H. Siewert. Zür theorisch technischen Beurteilung des Mhlen-prozesses moderner Mahlmaschinen. Das Papier 20(1):4–14, 1966.

9. J.-C. Roux. Review Paper on pulp treatment processes. In The Science of Paper-making, Trans. 12th Fund. Res. Symp., (ed. FRC), pp19–80, Oxford, 2001.

10. R. Bordin. Modélisation physique du fonctionnement d’un raffineur de pâte àpapier: description hydrodynamique de l’action du raffineur sur les fibres, Ph-Dthesis of Grenoble Institute of Technology, 2008.

11. R. Bordin, J.-C. Roux and J.-F. Bloch. Global description of refiner plate wear inlow consistency beating. Nordic Pulp and Paper Research Journal 22(4): 529–534,2007.

12. R. Bordin, J.-C. Roux and J.-F. Bloch. New technique for measuring clearance inlow-consistency refiners. Appita Journal 61(1):71–77, 2008.

13. J. Lumiainen. New theory can improve practice. Pulp and Paper International32(8):46–54, 1990.



THE NET NORMAL FORCE PERCROSSING POINT: A UNIFIED

CONCEPT FOR THE LOWCONSISTENCY REFINING OF

PULP SUSPENSIONS


Laboratoire de Génie des Procédés Papetiers, UMR CNRS 5518, GrenobleINP-Pagora, 461 rue de la Papeterie, 38402 Saint Martin d’Hères, France

Roger Gaudreault Cascades R&D

Why do you use the term “cutting kinetics” when you have not discussed thetime effect? Surely, kinetics should involve time?

Jean-Claude Roux

We have presented a study at a net specific energy consumption of 150 kWh/tonne, but it is clear that the effect can be obtained also for any level of netspecific energy. This means, on our installation, the time, because we areconducting constant net power trials. So we use the term “cutting kinetics”.

Stefan Lindström Mid Sweden University

I was wondering what parameters do you need to keep constant in order tomaintain this linear relation during refining? For example, moisture contentand similar properties.

Jean-Claude Roux

If I correctly understand your question, we have a line where all the points arealigned only due to the fact that the refining intensity reveals the physical

14th Fundamental Research Symposium, Oxford, September 2009

Transcription of Discussion

phenomena in the cutting kinetics of fibres. In statistics when you have anuncertainty on a typical phenomenon, you have clouds of points which arespread out. If you manage to properly understand the system, you willrestrict the clouds to a line. It is the purpose of my graphical comparison.If our tool is a correct tool for understanding the kinetic phenomena, thenall points should be aligned. We will have obtained a relationship betweenoutput and input.

Stefan Lindström

Yes, I understand but what if you changed something else like the contents ofmoisture in the system, or the geometry: would the linear relation still hold?

Jean-Claude Roux

If you change, for example, the bar crossing angle, this will have an effecton the formula because it will change the net normal force per crossingpoint. Suppose you change the metal of the bars by changing plates, this willproduce a change of the global friction coefficient. Suppose, you usedwounded bars or sharp bars, this will produce a change of the global frictioncoefficient. So we believe that actually we have the knowledge of the phenom-ena with this formula. If you change, for example, the consistency, you willget also a change in the global friction coefficient. This global friction co-efficient is a concept which seems very powerful for describing refiningeffects on fibres. I have presented to you only the results on cutting effects,but we could also use the concept to explain hydration, with the WRV, or theSchopper-Riegler level of the pulp.

Warren Batchelor Monash University (from the chair)

It was not quite clear to me how you are measuring the global frictioncoefficient?

Jean-Claude Roux

That is a very difficult question. The global friction coefficient in fact can bedetermined from the net power, but also, in the calculation we presented,from the normal force. So, our refining installation is equipped with a specificsensor for the normal force. At the beginning, I studied refining phenomenaas hydrodynamical and I was very interested by the load, which is exactly thesame as the load with the plane. It is a bearing load which is in fact very close

Session 1

Discussion

to phenomena that we find in hydrodynamics, making it very important.Another important quantity of course is the gap clearance. We have pre-sented a lot of publications on this subject, it is very difficult to measure.

Juha Salmela VTT

You are using net power. You have friction and other losses. Have youthought about measuring directly the forces on the gap or on the bar itself ?

Jean-Claude Roux

Good question. In fact, we have measured both. We measured on the axis, onthe shaft, but we also have seen the distribution of the normal force in thecorona, in the annulus. It is a very important point because from the input tothe output of the disk element annulus, you have different forces which areexerted on fibres, and different refining intensity. So, we have proposed onlyone refining intensity but in fact the raw material receives a distribution ofrefining intensity inside the disc annulus. So, as you can see, the area is openfor future work, many years of research, and many publications.

Wolfgang Bauer Graz University of Technology

Could we just go back to the parity diagram again, because I did not fullyunderstand how you calculated the average fibre length shown in thediagram?

Jean-Claude Roux

The parity diagram (figure 14 in the paper in the proceedings, ed.) comparesthe calculated fibre length (with net normal force per crossing point as anestimate of refining intensity) and measured length. You will recall that, foreach refining intensity, the model which seems to be a good candidate for ourdata is a parabolic curve for the variation of fibre length with net specificenergy consumption. So, for trial number k (at one refining intensity), wehave two coefficients ak and bk which can be determined, allowing us tointerpolate a fibre length at 150 kWh/tonne. This calculated fibre lengthallows us to see directly the refining intensity. We know the refining intensityfor each trial using several different measures, and we can plot these againstthe calculated fibre lengths. That is why we produce the parity diagram, tocompare this straight-line model of fibre length with the measured values. Wecan produce it with the other measures of refining intensity, but it does notwork so well.

14th Fundamental Research Symposium, Oxford, September 2009

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